A bird species in danger of extinction has a population that is decreasing exponentially left parenthesis upper a equals upper a 0 e superscript kt right parenthesis. six years ago the population was at 1400 and today only 1000 of the birds are alive. once the population drops below 100 , the situation will be irreversible. when will this happen

This will happen in 39 years.

Explanation:

The population of the birds varies as A = A. e^kt

The population of birds fell from 1400 from 1000

Time it will take for the population to fall below 100 = x years.

when t = 0, population = 1400

t = 3; Population = 1000

Therefore:

1400 = 1000e^5k

e^5k = 1400/1000

k = (In 1.4) / 5

we need to find x, such that

1400/1000 = (e^xk)

14 = (e^xk)

In (14) = kx

x = 5In (14) / In (1.4)

x = 39 years